Prime numbers play an extremely important role in modern mathematics. Apart from still being the object of intense research activity, their applications in banking and security underline a key phenomenon: in the modern world, useful applications of mathematics often come from very "pure" abstract theories. Curiously, despite their undeniable importance, prime numbers are largely absent from school curricula. Prime numbers are typically encountered in Year 7. There one looks at the...

Topics: ERIC Archive, Numbers, Modern Mathematics, Mathematics Instruction, Cairns, Grant

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Feb 21, 2017
02/17

by
JAGJIT SINGH

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GREAT IDEAS OF MODERN MATHEMATICS, JAGJIT SINGH, KALINGA AWARDEE

Topics: GREAT IDEAS OF MODERN MATHEMATICS, JAGJIT SINGH, KALINGA AWARDEE

This curriculum bulletin is the second part of "Mathematics--Pre-Kindergarten, Kindergarten, and Grade One." This is a developing curriculum program that incorporates the pre-kindergarten into the educational system and reorganizes mathematics materials in the early childhood years. The materials in this bulletin deal with numbers and operations with numbers, early levels of number-line concepts, geometric concepts, and fractional parts. Included also is a suggested plan for...

Topics: ERIC Archive, Arithmetic, Curriculum Development, Elementary School Mathematics, Guidelines,...

Included in this set of materials is a description of an instructional model for elementary school mathematics, a curriculum guide developed by the elementary school teachers of the California Area School District, scope and sequence guides, and a teachers manual. The instructional model includes the use of pretests, posttests, prerequisites and behaviors as they relate to the idea of flexible grouping in elementary school mathematics. The teachers manual contains materials for each content...

Topics: ERIC Archive, Curriculum Development, Curriculum Guides, Elementary School Mathematics,...

Part 2 of Course I includes a study of set theory, transformations of the plane; properties of lines, planes, line segments and angles; elementary number theory; and rational numbers. Decimal fractions, ratio and proportion, percent, and presenting data using graphs are also presented. (FL)

Topics: ERIC Archive, Algebra, Curriculum Development, Graphs, Instructional Materials, Modern Mathematics,...

The writer reminds readers that the polemics of reform frequently portray the realm of teaching and learning in more extreme terms than is really necessary. Likening calls for educational reform to scientific revolutions sparked by Kuhn, Darwin and Copernicus, that jettison completely the assumptions and premises of the theories they replace, Bond expresses concern that such approaches in education may result in acceptance of innovation based on faulty premise, and that there may be little hard...

Topics: ERIC Archive, Modern Mathematics, Phonics, Educational Change, Reading Instruction, Teaching...

In this 1967 booklet, influences of technology, the non-achiever and the culturally disadvantaged, and the revolt against formalism are discussed in relation to the modern mathematics curriculum. Some projects and school programs described include PLATO, the Nuffield Project, the Nova School Program, Advanced Placement Program, and teacher education programs. Materials (such as mirror cards, attribute blocks, and textbooks), methods (CAI, math labs, discovery learning), curriculum (new topics...

Topics: ERIC Archive, Curriculum, Instruction, Instructional Materials, Mathematics Education, Modern...

The following topics are discussed in this state handbook: (1) characteristics of a modern math program (structure, vocabulary, correctness); (2) teacher preparation (program descriptions and source material lists for inservice education and the CUPM recommendations for training math teachers); (3) initiating a modern program in mathematics in a particular school system (programs for different types of students, resources for administrators, guidelines for improving programs); (4) mathematics...

Topics: ERIC Archive, Curriculum, Curriculum Guides, Elementary School Mathematics, Instruction, Modern...

Written to provide some basic information for parents about the New York State Elementary School Mathematics Program, this pamphlet briefly discusses techniques of number operations on the whole numbers, number systems, sets, and geometric concepts. (DT)

Topics: ERIC Archive, Curriculum, Elementary School Mathematics, Geometric Concepts, Instruction,...

The first part of Course III focuses on matrix algebra, graphs and functions, and combinatorics. Topics studied include: matrices and transformations, the solution of systems of linear equations, matrix multiplication, matrix inversion and a field of 2 x 2 matrices. The section on graphs and functions considers regions of the plane and translations, functions and solution of equations, operations on functions, and bounded functions and asymptotes. The chapter on combinatorics discusses such...

Topics: ERIC Archive, Algebra, Curriculum Development, Instructional Materials, Mathematics, Modern...

This experiment attempted to teach abstract mathematics fo college freshmen with A.C.T. scores less than 15 in a three semester terminal course sequence. The course content included a formal mathematical language, set theory, Boolean Algebra, relations and functions, operations, cardinals and ordinals, the rational numbers, and college algebra. The tests for this course consisted of problems not previously encountered in class as well as "open questions" of the "prove or...

Topics: ERIC Archive, Academic Achievement, College Mathematics, Instruction, Low Ability Students,...

This investigation attempted to determine how pupil attitudes toward mathematics might be changed by introducing the new Laidlaw Series in the Moscow Elementary School during the academic year of 1965-66. The Kansas Arithmetic Inventory for Elementary Pupils was administered as a pretest prior to the introduction of the new text and a post-test after the new modern mathematics text had been used for seven months. The result of the experiment, assuming the validity of the arithmetic inventory...

Topics: ERIC Archive, Achievement, Elementary School Mathematics, Instructional Materials, Mathematics,...

This volume is an experimental edition for a high school course in the theory of matrices and vectors. One of the basic aims is to demonstrate the structure of mathematics. Another criterion is to provide some tools that will be useful in the student's transition from school to college. A last objective is that the intellectually vigorous students may obtain an idea of what constitutes "mathematical research." The five chapters found in the text are: (1) Matrix Operations; (2) The...

Topics: ERIC Archive, Algebra, Experimental Programs, Mathematics Curriculum, Mathematics Instruction,...

This is Part 1 of the first course in a series which focuses on building fundamental mathematical structures. The arithmetic studied in elementary school along with modular arithmetic is examined and set notation and mappings of sets are presented. Mathematical group structures are introduced. Points and numbers are related both on a line and in a lattice framework. (FL)

Topics: ERIC Archive, Algebra, Curriculum Development, Instructional Materials, Modern Mathematics, Number...

The second part of Course III includes a study of probability, polynomial, rational and circular functions, and informal space geometry. The chapter on probability presents such topics as probability measure, outcome sets and events, and overview of topics studied in Courses I and II. Chapters on functions include polynomial algebra concepts and basic trigonometry. The space geometry chapter generalizes the notions of incidence, parallelism, perpendicularity, and coordinate systems to three...

Topics: ERIC Archive, Algebra, Curriculum Development, Geometry, Instructional Materials, Mathematics,...

Reports on the development of a course in modern mathematics for elementary school teachers. The subject matter for the course is concentrated on whole numbers, integers, and rational numbers. Ideas of logic and set theory are brought into the discussion incidently as needed for developing the number systems. Part 1 of the course is a brief essay on "What is a Teacher." Part 2 consists of four chapters on Number Systems. Each chapter is divided into sections, and each section is...

Topics: ERIC Archive, Curriculum Development, Elementary School Teachers, Instructional Materials,...

This is the sixth in a series of ten self-contained units designed for use by students in ninth grade general mathematics classes. This unit is divided into eight sections dealing with different types of mathematical thinking. Some topics presented include functions, permutations and combinations, symmetry, inductive thinking, and logic. Though the topics are standard they are dealt with in non-traditional methods emphasizing discovery learning. Included are many diagrams, exercises, and topics...

Topics: ERIC Archive, Discovery Learning, Grade 9, Instructional Materials, Mathematics Materials, Modern...

The author defines individualization in instruction and suggests possible elements of individualization in mathematics classes. Some described elements include (1) individual responses to common assignments, (2) individual paths to the same objectives, (3) different objectives for different students, (4) different completion times for the same objectives, and (5) individually selected problems. He then describes programs for individualization now in existence. These include Individually...

Topics: ERIC Archive, Curriculum, Experimental Programs, Individualized Instruction, Instruction, Junior...

This publication provides reports from several mathematics educators on the gains that have been made, and the problems still unsolved, related to curriculum activities in mathematics. Answers to certain key questions which are basic in curriculum development are explored--(1) What are the goals of teaching mathematics, (2) What mathematical ideas, skills, attitudes, and habits can be most effectively developed at a given grade level, (3) How should programs be varied to provide for different...

Topics: ERIC Archive, Curriculum, Educational Change, Educational Objectives, Instruction, Mathematics,...

Reported are three studies which have been completed since the inception of a collaboration between the Inglewood Schools and UICSM. These include a comparison by a matched-pairs design, a total group comparison in which covariance analysis provided statistical control, and an item analysis of the tests which obtained difficulty indices for the UICSM experimental group and the comparison group on each item. Forty matched-pairs of UICSM and non-UICSM students were formed on three variables and...

Topics: ERIC Archive, Academic Achievement, Algebra, Instruction, Modern Mathematics, Secondary School...

This paper asserts that the key to algebra reform is to integrate algebraic reasoning across all grades and all topics, to "algebrafy" school mathematics. The distinction is made between algebra "the institution" and algebra "the web of knowledge and skill," which is also clarified. Finally, suggestions are made as to how the educational community might work towards a genuine algebra for all. The appendix provides concrete, classroom-based illustrations of the...

Topics: ERIC Archive, Algebra, Educational Change, Elementary Secondary Education, Learning Strategies,...

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) Srinivasa Ramanujan; (2) Minkowski; (3) Stefan Banach; (4) Alfred North Whitehead; (5) Waclaw Sierpinski; and (6) J. von Neumann. (MP)

Topics: ERIC Archive, Curriculum, Enrichment, History, Instruction, Mathematicians, Mathematics Education,...

The author describes the concept of Randolph diagrams (R-diagrams) which is a scheme for simplifying set-theoretic and/or logical expressions. Several applications of R-diagrams are presented. [Not available in hardcopy due to marginal legibility of original document.] (FL)

Topics: ERIC Archive, Curriculum Enrichment, Mathematical Concepts, Mathematical Logic, Mathematics,...

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) Laplace; (2) Carl Friedrich Gauss; (3) Wolfgang and Johann Bolyai; (4) Evariste Galois; and (5) Josiah Willard Gibbs. (MP)

Topics: ERIC Archive, Curriculum, Enrichment, History, Instruction, Mathematicians, Mathematics Education,...

Assessed was the performance of subjects who had been exposed to transformational geometry treatment. The performance test consisted of geometry achievement and spacial ability measures. Second and third grade subjects were randomly assigned to experimental and control groups. The experimentals received a twelve lesson treatment and the controls a one lesson treatment concerning rigid motion and congruence concepts. Pretest and posttest results indicated that the experimentals performed...

Topics: ERIC Archive, Elementary School Mathematics, Geometric Concepts, Geometry, Instruction,...

This is Part 1 of the second course in a series which focuses on building fundamental mathematical structures. Topics considered in this book include: an introduction to mathematical logic and mathematical proof, a continuation of the study of groups, an introduction to axiomatic affine geometry, fields, the real number system, and coordinate geometry. The discussion of groups contains an example of a non-commutative group, theorems about groups, and the concept of isomorphism. Axioms for an...

Topics: ERIC Archive, Algebra, Curriculum Development, Geometric Concepts, Geometry, Graphs, Instructional...

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the nature of mathematics; (2) mathematical inutility and the advance of science; and (3) logic. (MP)

Topics: ERIC Archive, Curriculum, Enrichment, Instruction, Logic, Mathematical Applications, Mathematics...

This curriculum bulletin is one of a planned series of bulletins designed to meet the needs of teachers and supervisors who are working to improve the achievement level of mathematics in the schools. The eighty sequential units of this bulletin are organized into 3 categories - (1) Sets, number and numeration, (2) Operations, and (3) Geometry and measurement. A "Note to Teacher" is included in several of the units to provide further clarification of mathematical concepts connected...

Topics: ERIC Archive, Arithmetic, Curriculum Development, Elementary School Mathematics, Geometry, Grade 5,...

This is the ninth in a series of ten self-contained units designed for use by students in ninth grade general mathematics classes. This unit is divided into six sections dealing with different concepts involving positive and negative numbers. Some concepts presented include positive and negative integers, addition and subtraction, multiplication, absolute value, and rational numbers. Though the topics are standard they are dealt with in non-traditional methods emphasizing discovery learning....

Topics: ERIC Archive, Algebra, Discovery Learning, Grade 9, Instructional Materials, Integers, Modern...

Described is the development of an approach to the algebra of real numbers which includes three areas of mathematics not commonly found in grade 9--the theory of limits of infinite sequences, a frequent use of Cartesian co-ordinates, and algebra of matrices. Seventy per cent of the course is abstract axiomatic algebra and the remaining portion includes intuitive mathematics. The segment of the course, which is based on intuition, includes a brief consideration of problems of measurement and...

Topics: ERIC Archive, Algebra, Curriculum Development, Curriculum Guides, Grade 9, Mathematics, Modern...

Topics included in Part 2 of Course II are: real functions; descriptive statistics; transformations in the plane; length, area, and volume; combinatorics; and mass points. The chapter on real functions includes a discussion of properties of functions, composition of functions, inverses of functions and other topics. The chapter on descriptive statistics discusses the graphical representation of sets of data, summation notation, the arithmetic mean, measures of dispersion, and Chebyshev's...

Topics: ERIC Archive, Curriculum Development, Geometric Concepts, Instructional Materials, Mathematics,...

The concept of function is central to the teaching and learning of mathematics. As a mathematical notion, the concept of function is fundamental, yet powerful, and is a unifying theme that is found running throughout most branches of mathematics. Until quite recently, when it came to the elementary transcendental functions it was commonly perceived that everything there was to know in this domain had been discovered long ago. Recent research efforts in the field of special functions (Corless,...

Topics: ERIC Archive, Mathematics Teachers, Modern Mathematics, Mathematics Instruction, Educational...

This volume is based on reports from representatives of eight countries concerning current mathematics curricula for the primary grades with emphasis on inclusion of topics in "new mathematics." The eight countries are: Austria, Belgium, Switzerland, Federal Republic of Germany, France, United Kingdom, Ireland, and Finland. A chronological outline of reform in mathematics education in these countries is presented. The major portion of the volume is organized around five major topics:...

Topics: ERIC Archive, Comparative Education, Curriculum, Educational Change, Elementary Education,...

The process of change and development of the mathematics curriculum in the United States is reviewed. Fundamental changes of implemented curricula from 1960-1980 are discussed in the light of the considerable efforts at reform during the 1950's and 1960's. Elements of the educational system are mapped out, and reasons for the lack of effective implementations of reform are suggested. (MP)

Topics: ERIC Archive, Curriculum Development, Educational Change, Mathematics Curriculum, Mathematics...

A pilot study was conducted of the understanding of prospective elementary school teachers of mathematical concepts. Purposes were to test the diagnostic instrument used to measure comprehension of concepts and to determine whether American College Test mathematics scores of student teachers could be used to predict ability to understand concepts used in new math in the elementary school. Ss were 46 student teachers to whom the Modern Mathematics Understanding Test, Multilevel Education was...

Topics: ERIC Archive, Elementary School Mathematics, Mathematical Concepts, Mathematics Teachers, Modern...

This study interprets and evaluates elementary mathematics research literature and current teaching practice. The list contains three related documents: (11-A) gives answers from research on elementary mathematics. It is the authors synthesis and interpretation of research findings in question-and-answer format; (11-B) offers generalizations and implications on elementary school mathematics which the authors believe to be clearly substantiated by research; (11-C) lists current research...

Topics: ERIC Archive, Elementary School Mathematics, Elementary School Teachers, Mathematical Concepts,...

The purpose of this study was to evaluate the appropriateness and effectiveness of current high school mathematics curricula for students in technical and vocational education programs. Students in 21 Wisconsin high schools were surveyed; administrators and chairmen of mathematics departments in these schools were also interviewed. Results indicated that most schools require one course in mathematics for graduation, although schools are reevaluating the requirement. The majority of schools were...

Topics: ERIC Archive, Curriculum, Curriculum Evaluation, Educational Needs, Evaluation, Graduation...

This guide for parents explains the objectives of the modern mathematics being taught in the schools and discusses the teaching methods being used. A few of the elementary concepts of modern mathematics (number lines, searching for patterns, different ways of analyzing problems, number bases, and sets) are briefly explained and justifications are given for their inclusion in the modern mathematics curriculum. Short descriptions of the Madison Project, Suppes' Projects, University of Illinois...

Topics: ERIC Archive, Curriculum, Elementary School Mathematics, Instruction, Mathematical Concepts,...

This publication is part of a series of guides written by Pennsylvania's Department of Public Instruction and is designed to present some of the unifying concepts in mathematics to elementary teachers. This pamphlet discusses the commutative, associative, and closure properties for addition and multiplication of whole numbers, and the distributive property. Numeration systems, including decimal and non-decimal systems, are briefly described. Short exercise sets are included for each section,...

Topics: ERIC Archive, Curriculum, Elementary School Mathematics, Instruction, Mathematics Education, Modern...

The life cycle of "new math" is fertile ground for the study of the diffusion of an innovation. New math arrived in 1958 to save the day for America after the Soviet Union launched Sputnik, the first successful space flight in 1957. In a period of 16 years an entire diffusion cycle was completed throughout the entire educational system of the United States. In some cases, new math was a success; in others it was a failure. The success of the classic diffusion of innovations model in...

Topics: ERIC Archive, Case Studies, Communication Research, Diffusion (Communication), Educational Change,...

Reported are the results of an experimental course taught at the ninth grade level. The course included both modern and traditional topics in algebra. Presented are a rationale for the course, a list of the topics included in the course, a description of instructional techniques and methods used in presenting and developing some of the main ideas in the course. It is believed that the course is different from other modern ninth grade algebra courses in these respects: (1) the inclusion of the...

Topics: ERIC Archive, Algebra, Curriculum, Curriculum Development, Discovery Learning, Grade 9,...

This supplementary modern mathematics textbook is to help in-service teachers to broaden their background in mathematical concepts and ideas for grades 1 through 9. This in-service course was written with two basic objectives: (1) to help teachers to become familiar with some of the newer mathematical ideas and concepts for grades 1 through 9, and (2) to suggest ways in which creative learning can become part of the school program in mathematics. Materials from rectangular coordinates, the...

Topics: ERIC Archive, Algebra, Arithmetic, Curriculum Development, Discovery Learning, Elementary School...

This workbook for elementary teachers presents basic definitions and examples in the areas of set theory, numeration systems, fundamental operations and geometry. Text organization does not use programming frames. Answers to examples are included in a separate section. (DT)

Topics: ERIC Archive, Arithmetic, Elementary School Mathematics, Geometry, Instructional Materials,...

A workshop to develop a program for training primary school teachers was convened in 1969 by the Regional Centre for Education in Science and Mathematics (RECSAM) in Penang, Malaysia. Countries participating in the conference were Indonesia, Malaysia, Singapore, South Vietnam, Thailand, Phillipines, and Ceylon; consultants from the United States and Britain were also in attendance. The major outcome of the conference was a detailed description of a course designed to improve teachers'...

Topics: ERIC Archive, Curriculum, Curriculum Development, Elementary Education, Elementary School...

It is extremely difficult to extend in a natural way the concepts developed in high school geometry to motivate the concepts of trigonometry. To solve this difficultry, the author defines "sensed angles" as ordered pairs of rays and makes appropriate definitions which yield the familiar angle properties of plane geometry. He then shows how this definition also yields the familiar results of trigonometry. (Author/CT)

Topics: ERIC Archive, Geometric Concepts, Geometry, Instruction, Mathematical Concepts, Mathematical...

Behavioral differences between school superintendents who achieve their positions through promotion in the home district (place bound) and those who achieve their positions through movement from one school system to another (career bound) were analyzed by means of interviews with 61 superintendents in one county. The study examined the rate of adoption of educational innovations, positions in the social structure of school superintendents, and reference group orientations. The data reveal that:...

Topics: ERIC Archive, Administrator Characteristics, Educational Innovation, Modern Mathematics,...

THIS IS A FINAL REPORT ON THE DEVELOPMENT AND PRESENTATION OF FOUR COLLEGE COURSES BY COMPUTER TELEPROCESSING FROM APRIL 1964 TO JUNE 1967. IT OUTLINES THE PROGRESS MADE TOWARDS THE PREPARATION, DEVELOPMENT, AND EVALUATION OF MATERIALS FOR COMPUTER PRESENTATION OF COURSES IN AUDIOLOGY, MANAGEMENT ACCOUNTING, ENGINEERING ECONOMICS, AND MODERN MATHEMATICS. EQUIPMENT CONFIGURATION IS DESCRIBED, AND A DIGEST OF THE COURSEWRITER LANGUAGE, PROGRAM SAMPLES, AND OUTLINES OF MATERIALS USED FOR THE FINAL...

Topics: ERIC Archive, Accounting, Audiology, College Curriculum, College Students, Computer Assisted...

Seventh grade students (N=9) from a small rural school in Ridgway, Colorado were exposed to a teacher-developed individualized program in modern math during the 1962-63 school year and again the following year. The students were divided into an average and above group and a below average group; group assignments were determined by IQ scores, the California Arithmetic Test for Junior High (grade placement and percentile standing), and consultations with the student's former math teacher....

Topics: ERIC Archive, Academic Achievement, Aptitude, Comparative Analysis, Grade 7, Individualized...

This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and social activities; (2) how analytic/algebraic combinatorics is similar to analytic/algebraic geometry; (3) basic combinatorial structures with...

Topics: ERIC Archive, Curriculum Development, Higher Education, Interdisciplinary Approach, Mathematical...

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Aug 22, 2017
08/17

by
Ling Anderson

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Real projective space RP^2 is the core of a ph.d program in pure mathematics and is ubiquitously taught in all classes, topology, algebraic geometry, differential geometry, etc. It's very interesting because if you walk on a certain path on RP^2, you will come back mirror reversed. I will try to explain. I just realized its even harder to explain math without preparing beforehand! You can learn more on wikipedia: https://en.wikipedia.org/wiki/Real_projective_space...

Topics: Youtube, video, People & Blogs, real projective space, euclidean space, RP2, RP^2,...